Anomaly Detection in Graph Signals With Complex Wavelet Packet Correlation Mining

Data generated by network-structured applications, such as sensor networks or communication networks, typically reside on complex and irregular structures. These data necessitate specific graph signal processing tools to harness their characteristics. Detecting anomalous events in graph signals is significant in enhancing reliability of systems, where anomalies often activate localized groups of vertices. In this paper, we introduce a novel approach, the Joint Graph Wavelet Canonical Correlation Analysis, for detecting anomalies in graph signals through cooperative filtering while identifying their locations. This approach conducts canonical correlation analysis on graph signals to achieve data fusion within the wavelet domain while accounting for the graph topology. Subsequently, we devise an optimization algorithm specifically tailored for anomaly detection in graph signals. Finally, we illustrate its effectiveness through numerical simulations on synthetic data and by presenting test results from a multi-microphone network.